I have heard creationists claim on multiple occasions that the Cambrian explosion disproves evolution. For example, Lee Strobel in this video claims that the all the phyla appeared at once, independently, and therefore they were created.
First we have to understand what the Cambrian explosion is. The Cambrian explosion occurred about 530 million years ago and lasted around 80 million years. (EDIT: Quasar brought to my attention that the exact length of time of the Cambrian explosion is under dispute. However, the lowest estimate is still around 5 million years.) During this time, many of the phyla or general body types first appeared for animals. Before the Cambrian explosion, very few fossils exist of multicellular creatures, and life appears to be mainly composed of single cell organisms.
However, not all phyla made their appearance during the Cambrian explosion. Land-based life such as flowers, ferns, etc... developed much later.
While fossils from the Cambrian explosion and Precambrian are rare, evidence exists that all these body types did not evolve completely independently. All animal phyla, for example, share many common characteristics. They are all triploblastic (the embryo forms in 3 layers), bilatteral (have left and right halves) coelomates (have internal body organs). Therefore, evidence of common ancestry is suggested in the formation of these early phyla groups.
More importantly, geologists found fossils predating the Cambrian explosion of burrows which require a digging mechanism and multicellular creatures. So the idea that creatures found in the Cambrian explosion arose without precedent is simply untrue. Life had been developing into more complex, multicellular forms in the Precambrian.
The easiest way to explain the Cambrian explosion is through the theory of punctuated equilibrium. According to the theory, the evolution of most sexually-reproducing creatures occurs in short bursts followed by long stretches of few changes.
While the theory of punctuated equilibrium may have been over-sold, the idea that changes to the environment spur evolutionary development is well understood by biologists. After all, the information for evolution comes from the environment - change the environment, change the creature.
It just so happens that the amount of oxygen in Earth's atmosphere dramatically rose during the time of the Cambrian explosion, giving animals more oxygen to work with. This extra oxygen could have enabled creatures to grow larger than ever before without suffocating their body parts due to a lack of oxygen.
So while much remains to be learned about the Cambrian explosion, the idea that it somehow proves that omnipotent deity magically created life on Earth is a very much unwarranted.